Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity

1. Atul Kapur akapur@rsmas.miami.edu Thermal Equilibrium of the Atmospherewith a Given Distribution of Relative Humidity from a paper by S. Manabe and Richard T. Wetherald 1966

2. Concept of Thermal Equilibrium No atmosphere Fixed emissivity and absorptivity at a given layer But in reality Absolute Humidity is a strong function of temperature? Fixed distribution of absorbers including water vapor (or Absolute humidity) (Manabe and Srickler, 1964)

3. Why fixed Relative Humidity? DJF Strong seasonal variation in Absolute Humidity JJA Zonal-mean Absolute humidity (g kg-1) DJF Weak seasonal variation in Relative Humidity JJA Zonal-mean Relative humidity (%) (Peixoto and Oort, 1992)

4. Concept of Thermal Equilibrium No atmosphere Fixed emissivity and absorptivity at each layer But Absolute Humidity is a strong function of temperature? Fixed distribution of absorbers including water vapor (or Absolute humidity) (Telegadas and London, 1954) Fixed distribution of Relative humidity (Manabe and Srickler, 1964) (Manabe and Wetherald, 1967)

5. Implications of fixed Relative Humidity • Mixing ratio is now allowed to change with change in temperature • Another degree of freedom PARTIALLY released • Constrained by the condition of fixed Relative Humidity

6. Other input distributions • Mixing ratio of CO2 is assumed to be constant (300 ppm by volume) (Herring and Borden, 1965) (London, 1956) Cloud characteristics Ozone

7. Pure radiative Equilibrium(no convection) Radiative (Fixed abs. humidity) Cooler Atmospheric Temperature + Fixed relative humidity Radiative (Fixed relative humidity) Less greenhouse effect Further temperature drop at the surface Less moisture Radiative-Convective (Fixed relative humidity) Self Amplification effect (Hergesell, 1919)

8. OLR dependence on humidity Effective heat capacity OLR OLR Fixed abs. humidity (I) Fixed RH with Cp dry (II) Fixed RH with effective Cp (III) Warmer Atmospheric Temperature + Fixed relative humidity OLR lesser (than in case of fixed absolute humidity) Increase in moisture in a given volume of air Increase in latent energy of air Slower Approach towards equilibrium Slower approach towards equilibrium Increase in height of effective source of OLR Lesser Radiative cooling Increase in effective heat capacity Approach of mean temperature towards equilibrium

9. Sensitivity to the value of Solar Constant OLR OLR Higher value of Solar constant + Fixed relative humidity Increase in temp. + But OLR less than expected Further inc. in temp. to increase OLR at top of atmosphere Higher sensitivity of temperature upon Solar constant

10. Sensitivity to the value of Solar Constant • For fixed RH, equilibrium temp. is almost twice as sensitive as for fixed absolute humidity • Difference in sensitivity decreases with temp. Fixed RH Fixed abs. humidity Surf Temp. Solar constant Mixing ratio of water vapor is lower at lower temperatures Self-amplification effect

11. Sensitivity to CO2 with fixed Relative humidity • More CO2 results in warmer troposphere and warmer surface • More CO2 results in colder stratosphere • Stratospheric temp. much more sensitive to CO2 than troposphere. Increase in temp. + OLR less than expected Inc. in CO2 + Fixed relative humidity Increased sensitivity to CO2 Sensitivity of temperature upon CO2 almost double as compared to fixed absolute humidity Doubling of CO2 raises the atmospheric temp. by 2 °C

12. Sensitivity to surface albedo with fixed Relative humidity • Larger albedo colder the temperature • Influence of surface albedo vanishes with height Sensitivity upon surface albedo almost double as compared to fixed absolute humidity

13. Points to “take home” • Time required for radiation-condensation relaxation is almost double than that required for radiation relaxation. • For fixed RH, sensitivity of surface temp. upon solar constant, cloudiness, surface albedo, and CO2 content is almost twice as compared to that for fixed absolute humidity • Doubling of CO2 with fixed relative humidity increases surface temp. by about 2.3°C.

14. Thank You